Polarizability of ultracold molecules in the rovibrational ground state of

Abstract

We study, both theoretically and experimentally, the dynamical polarizability $\alpha (\omega )$ of ${\mathrm{Rb}}_{2}$ molecules in the rovibrational ground state of ${a}^{3}{\Sigma }_{u}^{+}$ . Taking all relevant excited molecular bound states into account, we compute the complex-valued polarizability $\alpha (\omega )$ for wave numbers up to 20 000 ${{\rm{cm}}}^{-1}$ . Our calculations are compared to experimental results at $1064.5\;\mathrm{nm}$ ( $\sim 9400\;{{\rm{cm}}}^{-1}$ ) as well as at $830.4\;\mathrm{nm}$ ( $\sim 12\;000\;{{\rm{cm}}}^{-1}$ ). Here, we discuss the measurements at $1064.5\;\mathrm{nm}$ . The ultracold Rb _2 molecules are trapped in the lowest Bloch band of a 3D optical lattice. Their polarizability is determined by lattice modulation spectroscopy which measures the potential depth for a given light intensity. Moreover, we investigate the decay of molecules in the optical lattice, where lifetimes of more than $2\;{\rm{s}}$ are observed. In addition, the dynamical polarizability for the ${X}^{1}{\Sigma }_{g}^{+}$ state is calculated. We provide simple analytical expressions that reproduce the numerical results for $\alpha (\omega )$ for all vibrational levels of ${a}^{3}{\Sigma }_{u}^{+}$ as well as ${X}^{1}{\Sigma }_{g}^{+}$ . Precise knowledge of the molecular polarizability is essential for designing experiments with ultracold molecules as lifetimes and lattice depths are key parameters. Specifically the wavelength at $\sim 1064\;\mathrm{nm}$ is of interest, since here, ultrastable high power lasers are available.

Keywords

• cold molecules
• polarizability
• optical lattice